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International Conference on Numerical Analysis and Its Applications

NAA 2008: Numerical Analysis and Its Applications pp 580–587Cite as

A Two-Grid Algorithm for Solution of the Difference Equations of a System of Singularly Perturbed Semilinear Equations

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 5434)

Abstract

We propose a two-grid algorithm for implementation of a generalized A.M.Il’in’s scheme to a system of semilinear diffusion convection-dominated equations. To solve the nonlinear algebraic system of difference equations we use Newton method. We derive the difference scheme on a coarse mesh and, then using uniform interpolation, taking into account the boundary layers, we obtain the initial guess for an iterative method on a fine mesh. Estimates of the accuracy and the computational work are obtained. The main advantage of the proposed algorithm is the computational cost.

Keywords

  • Boundary Layer
  • Initial Guess
  • Newton Method
  • Coarse Grid
  • Boundary Layer Problem

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • DOI: 10.1007/978-3-642-00464-3_68
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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Rousse, Bulgaria

    L. G. Vulkov

  2. Institute of Mathematics, RAS, Siberian branch, Omsk, 644099, Russia

    A. I. Zadorin

Authors
  1. L. G. Vulkov
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  2. A. I. Zadorin
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Editor information

Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  2. FNSE, Department of Numerical Methods and Statistics, University of Rousse, 8 Studentska str., 7017, Rousse, Bulgaria

    Lubin G. Vulkov

  3. Department of Informatics and Mathematical Modelling, Technical University of Denmark, 2800, Kongens, Lyngby, Denmark

    Jerzy Waśniewski

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© 2009 Springer-Verlag Berlin Heidelberg

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Vulkov, L.G., Zadorin, A.I. (2009). A Two-Grid Algorithm for Solution of the Difference Equations of a System of Singularly Perturbed Semilinear Equations. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_68

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  • DOI: https://doi.org/10.1007/978-3-642-00464-3_68

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00463-6

  • Online ISBN: 978-3-642-00464-3

  • eBook Packages: Computer ScienceComputer Science (R0)